Relative Motion

The problem is:


I'm finding the first part difficult - my main problem being putting everything on one coherent diagram.

Also does $W \theta^{\circ} N$, mean west and then $\theta^{\circ}$ from west towards north?

great question
That will be my homework for tomorrow ...

...

Thought this question was being dealt with when I saw it had been replied to.




See attached. Our motorist is at M. The wind's true velocity is the line in red. Angles are a,b,c as I can't be arsed to try greek letters in Paint.

You will still need the odd bit of construction on top of the basic diagram, but looking at the formula you are aiming at, perhaps you can "guess" what it is.

Thanks for the reply. I solved the first part. Still not sure on the last part (true direction of the wind). I'm guessing that I need to draw another diagram with V_W common to all of them? (I've attached the diagram with the construction lines I added for the first part).

You already have the required diagram, just mark the angle for V_W (the red line).

Notice that y could be any positive value in your diagram, so you're not going to get a fixed value for the angle of V_W, it's going to be a function of one or more of the other angles.

The methodology will be similar to how you did the first part.

Unless I missed a trick.

I'm on part(a). I've attached my diagram so far (Where $C_0, B_0$ are the initial positions of the cruiser and battleship respectively, and $V_C$ is the velocity of the cruiser). I know that for closest approach $V_B$ must be perpendicular to the relative path but I don't get how to draw it.

Closest approach questions tend to be one of the most confusing, and I go back to first principles rather than remember a specific method.

The velocity of the cuiser is fixed.
The velocity of the battleship is fixed in magnitude, but can be at any angle.

See diagram:

So, subtracting the velocity of the battlehsip, the velocity of the cruiser relative to the battleship is represented by the green lines going to the red circle's perimeter. Note that since we're subtracting the velocity of the battleship, the corresponding radii are minus the velocity of the battleship.

We want the line of that relative velocity to approach as closely as possible to the battleship, hence the thicker green line is the one we want which is tangential to the circle, and the distance of closest approach being the line in blue.

It looks overly complicated, but take out the construction lines, and it looks a lot clearer.


Going back to your original question: Post #1. When drawing diagrams, it may help to build it up bit by bit. Be aware of bits that are fixed (e.g. relative position of two points), and bits that are subject to some restriction (angle given but not distance/velocity, or a variable angle), and bits that go anywhere. If you come to add a piece that doesn't make sense, look at the bits you've already put in, and see if you can adjust them so it does make sense.

I may have just about understood that, Thank you! . I will try some more questions and hopefully solve them.

if you ran out of questions

http://madasmaths.com/archive/maths_booklets/mechanics/m3_m4_relative_motion.pdf

Thanks - I'll try some of them tomorrow.